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The short and long-run determinants of the real exchange rate in Mexico
Antonia Lopez Villavicencio,Josep Lluís Raymond Bara
06.06
Facultat de Ciències Econòmiques i Empresarials
Departament d'Economia Aplicada
Aquest document pertany al Departament d'Economia Aplicada.
Data de publicació :
Departament d'Economia AplicadaEdifici BCampus de Bellaterra08193 Bellaterra
Telèfon: (93) 581 1680Fax:(93) 581 2292E-mail: [email protected]://www.ecap.uab.es
Octubre 2006
The short and long-run determinants of thereal exchange rate in Mexico
September 4, 2006
Running title: Real exchange rate determinants in Mexico
Antonia LOPEZ VILLAVICENCIO ‡ and Josep Lluıs RAYMOND BARA §
‡ Corresponding author. Departament d’Economia Aplicada.Universitat Autonoma de Barcelona
Edificio B, 08193 Bellaterra (Barcelona), Spain.Phone number: +3493 5813258/ Fax number: +34935812292
E-mail: [email protected]
§ Departament d’Economia i d’Historia Economica.Unitat de Fondaments de l’Analisi Economica.
Universitat Autonoma de Barcelona,Edificio B, 08193 Bellaterra (Barcelona), Spain.
Phone number: +3493 5811711/ Fax number: +34935812292
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The short and long-run determinants of the real exchange rate in Mexico
Abstract
This paper explores the real exchange rate behavior in Mexico from 1960 until2005. Since the empirical analysis reveals that the real exchange rate is not meanreverting, we propose that economic fundamental variables affect its evolution inthe long-run. Therefore, based on equilibrium exchange rate paradigms, we proposea simple model of real exchange rate determination which includes the relative laborproductivity, the real interest rates and the net foreign assets over a long periodof time. Our analysis also considers the dynamic adjustment in response to shocksthrough impulse response functions derived from the multivariate VAR model.
Keywords: real exchange rate, purchasing power parity, Balassa-Samuelson ef-fect, error correction models, bounds cointegration test.
JEL classification: C32, F31, F41, F49
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IntroductionThe evolution of the real exchange rate (RER) is a leading indicator of the strength ofan economy. For instance, foreign investment, capital flows or international trade are alldeeply influenced by the modifications that the real exchange rate can bring upon thegoods and capital markets.
Even more, because a higher real exchange rate implies ceteris paribus- that a coun-try’s exports are more expensive and its imports relatively cheaper, it is a measure ofrelative competitiveness of imported goods among countries. Thus, given its close linkwith competitiveness, it turns out to be a fundamental issue when dealing with economiccrises and booms.
Indeed, it has been for some time a question of important debate whether real devalua-tions are contractionary or expansionary. On the one hand, in the conventional textbookmodel, devaluations are suppose to increase competitiveness, increase production andexports of tradable goods, reduce imports, and thereby boost the trade gap, GDP andemployment (assuming the Marshall-Lerner condition holds). On the other hand, Dıaz-Alejandro (1963), Krugman and Taylor (1978) or Lizondo and Montiel (1989) showed thatthis positive effect could be offset by contractionary impacts in the non-tradable sector.
Even though it is not clear what are the effects of real devaluations in the economy, inthe last years, many developing and emerging market economies have resist devaluation,partly because of concerns that such a policy would be contractionary 1. This viewarises from the experience of countries such as Mexico, where, as showed in figure 1, realdepreciations (increases) of the peso have consistently been associated with declines inoutput, while real appreciations (decreases) have been linked to expansions.
In this sense, the Mexican case can result useful to understand some aspects of thefinancial crisis in some developing and emerging market economies for several reasons.First, the Mexican move toward flexible exchange rates implies the topic is of interest toother currency markets that did the same. Second, the debtor position of the Mexicaneconomy is shared by other emerging economies such as Brazil or Argentina. Third, theexchange rate in Mexico, as in other emerging economies, is extremely volatile relative todeveloped countries. Finally, many developing countries have also experienced a series ofexternal shocks, similar to the Mexican experience2.
It is not our aim here to study whether a currency depreciation would have a favorableor negative effect on economic growth and employment. Whatever the association is, it isclear that the behavior in the real exchange rate has important and lasting effects on theeconomy as a whole. As such, whatever determines the real exchange rate has importancein itself. It is precisely the purpose of our investigation to find these determinants.
We show evidence below that, at first sight, the real exchange rate in Mexico does notconverge to its purchasing power parity value. Therefore, the main proposition of our workis that it is determined by macroeconomic fundamentals. We study whether permanent(or persistent) changes in these factors can explain the lasting movements of Mexico’sreal exchange rate. The determinants are analyzed both in terms of their long-run andshort-run impact on the real exchange rate. The empirical strategy will thus involvecointegration analysis and error-correction modelling between the real exchange rate anda set of selected macroeconomic factors, namely the real GDP per capita differential, the
1However, the devaluation itself might be the result of, among others, incorrect policies and economicslowdowns as it was apparently the case in Argentina in 2001.
2In the 1980s, for example, these shocks included a steep rise in international interest rates, a slowdownof growth in the industrial world, and the debt crisis.
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net foreign assets position and the interest rate.The GDP and the capital account do not imply any problem for the cointegration
approach, since they are usually find to be not stationary variables. However, most ofthe time, studies avoid including the real interest rate in the analysis (see Joyce andKamas (2003), for instance), mainly because it is usually find to be a stationary variable.However, we believe that it would be a mistake not to include the interest rate differentialin the analysis. In other words, if the chosen measure of real interest rate is I(0), failure toincorporate it in the long-run cointegrating vector implicity sets the interest rate influenceon exchange rate to zero.
Hence, to take account of the statistical property of the interest rate we analyzethe relationship between the RER and the fundamentals within a bounds cointegrationprocedure (Pesaran, Smith, and Shin (2001)). This approach has the advantage thatit test the existence of a level relationship between a dependent variable and a set ofregressors, irrespective of whether the underlying regressors are purely I(0), purely I(1)or mutually cointegrated. Thus, we are able to present the definition and estimation ofthe fundamental (long-run) and short-run influences in a model for the real exchange ratein Mexico.
Another advantage of our paper is that, contrary to most of the studies that analyzethe real exchange rate dynamics in Mexico, we go further than the 1994 collapse of thepeso (i.e. the floating exchange rate regime). Indeed, if what we are trying to find are thelong-run determinants of the real exchange rate, it would be a mistake to consider only ashort period of time in the analysis. Thus, we explore Mexico’s real exchange rate withinan extended period of time (1960-2005).
The rest of the paper is organized as follows. In the following section we discuss sometheoretical propositions for the empirical work. Section 2 deals with the evolution of thereal exchange rates and the factors that, in principle, determine its evolution. In section3 we present the econometric methodology and empirical results. Section 4 offers closingcomments.
1 Modelling Real Exchange Rates
The literature that takes on to model and explain the real exchange rate (RER) behavioris very extensive. Nonetheless, even there are many propositions, there is no consensus onwhat are its major determinants. Broadly speaking, in accordance to how integrated themarkets are suppose to be, we may think of two distinct approaches. Indeed, the exchangerate can be thought as a monetary phenomena or, on the contrary, as a macroeconomic(real) phenomenon. It is, precisely, in this distinction where the two major approacheson exchange rate determination differ.
On one hand, the monetary approach assumes highly integrated goods and capitalmarkets; therefore, it commonly expects the RER to meet the purchasing power parity(PPP) value as a long-run equilibrium value. Under this approach, the equilibrium realexchange rate for a given country remains constant overtime . Therefore, if any evidencethe RER in a given country reaches its PPP value were to be found, then the PPP wouldturn out to be particularly useful because it could predict any over or under valuation.Otherwise, there would be no basis to state the RER is an equilibrium relationship thatmust be met in the long-run .
On the other hand, by rejecting the PPP theory as an equilibrium reference, themacroeconomic approach centers its attention on the role played by the (real) economic
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fundamentals in the determination of the exchange rate. So, this approach considers theequilibrium real exchange rate as a path on which an economy preserves both internaland external balance. As such, the equilibrium real exchange rate is not an immutablenumber; it is rather influenced by some real variables.
Under this approach, two main lines of research are distinguished. The first one,known as the balance of payments approach, highlight the underlying net foreign assetposition of a country. The second one, based on the Balassa-Samuelson approach, centersits attention in the sectoral (tradable-nontradable) balance.
The balance of payment approach, introduced by Nurkse (1945), is based on theadequacy of the current account to keep notional or equilibrium capital flows and keepin check saving-investment balances. In this framework, several notions of equilibriumexchange rates have been suggested. For instance, Williamson (1985) suggested the notionof Fundamental Equilibrium Exchange Rate (FEER), which is defined as the exchange rate”which is expected to generate a current account surplus or deficit equal to the underlyingcapital flow over the cycle, given that the country is pursuing internal balance as bestit can and not restricting trade for balance of payments reasons” (Williamson, p.14).A variant of the FEER is the Desirable Equilibrium Exchange Rate (DEER), proposedby Bayoumi, Clark, Symansky, and Taylor (1994) which assumes target values for themacroeconomic objectives, such as targeted current account surplus for each country.
Another approach to equilibrium exchange rate is the Behavioral Equilibrium Ex-change Rate (BEER) by Clark and MacDonald (1998). The BEER relies on observedlong-run relationships between the real exchange rate and a set of (long-run and mediumterm) economic fundamentals -derived from the determinants of saving, investment andthe current account- and a set of transitory factors affecting the real exchange rate in theshort run.
In the same line, the Macroeconomic Balance Framework, suggested by Faruquee,Isard, and Masson (1998) can be seen as a specification of the BEER approach since themacroeconomic fundamentals are derived from the determinants of saving, investmentand current account. Similarly, the Natural Real Exchange Rate (NATREX), introducedby Stein (1994), falls between the FEER and the BEER approaches. The NATREX is theexchange rate that allows to attain of both internal and external equilibrium. However,the current account is modelled as the result of saving and investment behavior, as in theBEER approach.
The second line of research, based on the works by Balassa (1964) and Samuelson(1964) relates the long run behavior of the real exchange rate with the productivityperformance of traded relative to non-traded goods. The idea is that if the productivityof the traded goods rises relative to that of non traded goods, the real exchange ratewill appreciate. A Balassa-Samuelson effect can be introduced either in the FEER orin the BEER approach by assuming the existence of two sectors in the economy. Theexternal equilibrium need then only applies to the tradable goods sector, whereas internalequilibrium must include a long-run productivity drift on top of short-to-medium-rundemand effects (see Edwards (1989)).
Following the previous propositions, Alberola, Cervero, Lopez, and Ubide (1999) andAlberola (2003) propose a theoretical model that encompasses both, the balance of pay-ments and the Balassa-Samuelson approach to real exchange rate determination. Thestarting point of the model is to decompose the exchange rate into two different relativeprices. The first one, the price of domestic relative to foreign tradables, captures the com-petitiveness of the economy and settles the evolution of the foreign asset position. On the
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contrary, the second one, which is the relative price of non-tradables relative to tradableswithin each country, plays a central role in adjusting excess demand across sector in theeconomy.
1.1 The macroeconomic fundamentals
Based on the idea of equilibrium exchange rate, we propose a model that encompassesboth, the external sector of the economy and the Balassa-Samuelson approach to realexchange rate determination. We identify three main fundamentals for the evolution of thereal exchange rate: the productivity differentials (proxied by the real GDP differential),the net foreign assets position (proxied by the accumulated current account) and the realinterest rate differential.
• Productivity differentials: The impact of productivity differentials is expected tofollow the Balassa-Samuelson (BS) doctrine. That is, larger increases in productivityin the traded goods sector are associated with a real appreciation of the currency ofa given country. The BS hypothesis may prove useful in a context like ours, sinceit tries to explain the recurrent deviations of the RER from a long-run value byrelating the currency appreciation with the different states of productivity growthof the countries.
• Net foreign assets: Until recently, the appreciation of the real exchange rate indeveloping or transition countries was assigned to a Balassa-Samuelson effect af-fecting the sector of tradables. However, whether this effect is strong is today asubject of controversy. Indeed, the collapse of the Bretton Woods system in the1970’s, the following volatility of currency markets and the recent integration of in-ternational financial markets make the capital flows crucial to understand exchangerates, output, employment, etc.
Even more, the reform strategies conducted in Mexico, in particular, and in most ofthe developing countries, in general, were characterized by strengthening money andfinancial markets, the macroeconomic stabilization (about inflation, public financeand foreign debt) and the liberalization of the markets (that is, prices and trade).All these features lead to the idea that something else, besides the comparisonof international levels of productivity, lies behind the recurrent deviations of theexchange rate from its PPP level.
Indeed, nowadays it is broadly accepted that trade and capital flows as well asimbalances between national savings and investment influence the exchange rate.Thus, a country’s foreign balance is another commonly used variable to explaincurrency behavior. For instance, in the context of the equilibrium exchange ratemodels the current account imbalance is one of the motives that can drive theexchange rate away from its equilibrium level (i.e. the level compatible with theharmonious running of the economy).
In this sense, there are several channels through which the stock of foreign assetscan influence the real exchange rate3. For instance, portfolio-balances considerationssuggest that a deficit in the current account creates an increase in the net foreign
3Lane and Milessi-Ferreti (1999) explore the theoretical link between the real exchange rate and thenet foreign assets, and provide evidence that the net foreign asset position is an important determinantof the real exchange rate for developing as well as developed countries.
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debt of a country, which has to be financed by internationally investors which, toadjust their portfolio, demand a higher yield. At given interest rates, this can onlybe achieve through a depreciation of the currency of the debtor country.
Also, the balance of payments channel assumes that a current deficit accumulatesnet foreign debts, for which interest have to be paid. To service these higher inter-est payments, the debtor country needs to strength its international price compet-itiveness. Thus, to increase the attractiveness of its exports, the country needs todepreciate its currency (see Maeso-Fernandez, Osbat, and Schnatz (2001)).
Summing-up, an increase in the capital flows will finance greater absorption anda larger current account deficit. This is obtained trough a real exchange rate ap-preciation, either trough raising prices or an appreciation of the nominal exchangerate. That is, the real exchange rate is expected to fall (to appreciate) when thestock of foreign assets rises4. Thus, it is our believe that in developing and emergingeconomies in general, and in Mexico, in particular, the RER is susceptible to capitalinflows and this is the case regardless of the exchange rate regime5.
• Interest rates: Perhaps one of the most widespread consensus across academic andpolicy-making cycles, is the solid relationship between interest rates and exchangerates. Conventional wisdom, based on the Mundell-Fleming tradition and Dornbush(1979) contribution, but also in more recent papers with risk neutral investors, isthat increases in any interest rate would appreciate the domestic currency6.
Theories based on portfolio balance suggest a close link between the exchange rateand the interest rates. The main idea is that the financial assets are not perfectsubstitutes among them. Then reducing the interest rate of one economy (domestic)in relation to another (foreign) creates an excess demand for foreign currency toprofit from the interest-rate differential. If domestic authorities do not intervenein the exchange-rate market, that excess demand will turn into a weaker domesticcurrency (a rise of the exchange rate or depreciation)7. Contrariwise, a rise ofdomestic interest rates, ceteris paribus, makes domestic assets more attractive toinvestors (national or foreign). This leads to a domestic currency appreciation asinvestors adjust their portfolios. Thus, a line of causality between interest-ratesand the exchange-rate is established not through the goods and services market butthrough the financial assets market8.
4While theoretically, capital flows would equal zero in the long-run, most less developed countries areexpected to be capital importers for the future, therefore most empirical studies of developing economiesuse a measure of sustainable capital flows rather than a zero capital account. Models of the RER in thesecountries often include capital flows as a determinant of the equilibrium real exchange rates (see Joyceand Kamas (2003)).
5Notice that if a country relies on foreign capital (or any other inward transfer) to keep high levelsof domestic absorption, it is natural for the RER to appreciate, regardless of the exchange rate regime.The adjustment occurs either through an appreciation of the nominal exchange rate under a floatingexchange rate system or through an increase in nominal prices of non-traded goods in a fixed exchangerate regime, or through a mixture of the two in an intermediate (fixed-but-adjustable) regime. Evidencealso suggests that, contrary to conventional wisdom, misalignments and currency ”crashes” are equallylikely under pegged and flexible exchange rate regimes.
6See Ogaki and Santaella (1999) for an empirical study on Mexico.7One could think of an expansive monetary policy where monetary authorities intervene in the market
buying peso-denominated bonds.8Although it is not our aim to analyze the relationship between the exchange rate and the term
structure of interest rate, theory suggests that it can be complicated and counterintuitive when investors
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2 Evolution of the real exchange rate and the macro-
economic fundamentals in Mexico
The belief that a competitive exchange rate encourages exports and hence growth is afundamental principle of the conventional wisdom of macroeconomic management (Kaminand Klau (1997)). Thus, for many years, policies were oriented towards keeping the realexchange rate highly competitive with the idea to prevent balance-of-payments crises andencourage output growth.
However, as we mentioned, many developing countries have resisted devaluations be-cause of concerns that such a policy would be contractionary. In Mexico, during the last45 years had a series of controlled (i.e. fixed, crawling, dual and target zone) exchangerate regimes, most of which ended in crisis and collapses. In the specific case of Mexico,each of the major crises over this period- August 1976, February and March 1982, July toNovember 1985, November 1987 and December 1994- was followed by a significant declinein economic growth (see figure 1).
[INSERT FIGURE 1]
Certainly, from 1960 until late 1970’s, Mexico lived through a long period of economicgrowth in which GDP grew faster than the population, reducing the income gap vis-a-visthe U.S. However, due to a strong foreign shock, this period of fast economic growthfell apart by the early 1980’s: From 1981 to 1986, GDP and GDP per capita fell 2%and 12% respectively. Thus, from that moment, any converging process on the incomelevels between the two countries came to halt and, once more, the gap widened while theMexican economy growth rate stagnated.
Indeed, as the figure shows, in 1981 Mexico had a cyclically high-level of output, ahighly appreciated real exchange rate and a large capital account surplus9. The onsetof the debt crisis in 1982 and the associated reversal of capital inflows led to a sharpreal devaluation of the peso and a marked contraction in output by 1983. Followingsome recovering of the economy and a reversal of real depreciation in 1984 and 1985,additional shocks led to the extreme real depreciation of the peso and depression ineconomic activity registered in 1986-87 (Kamin and Rogers (1997)). After an exchangerate based stabilization program launched in 1988 and regained access to internationalcapital markets, Mexico started to show a higher GDP, an appreciated peso and a largecurrent account deficit. Following the devaluation in 1994, a new reversal of capital flowsforced the economy back to where it had been in the early 1980’s.
In addition, prior to the 1994 devaluation, supporters of Mexico’s exchange rate strat-egy argued that the real exchange rate appreciation, and the associated widening of thecurrent account deficits, were signs of economic health, reflecting rising productivity andimproved prospects for the Mexican economy (Kamin and Rogers (1997)). The idea thatthe real appreciation could restrained economic growth was not an issue. However, after1994, the crisis highlighted the danger of allowing the real exchange rate to appreciatesubstantially in a world of high capital mobility. Since early 1995, however, the has beena slow process of recovery and real appreciation.
are risk averse. Ogaki and Santaella (1999), for instance, analyzes the effect of the term structure ofinterest rates on the real exchange rate for the Mexican floating exchange rate regime, finding the termstructure is indeed relevant. The one-month and the three-month interest rate differentials have theopposing effect on the exchange rate in Mexico.
9An increase (decrease) in the RER implies a depreciation.
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Figure 1: Evolution of the real exchange rate, GDP growth, GDP per capita differentials,current account (as % of GD), cumulative current account (as % of GD) and real interestrate differential. 1960-2005
2.1
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3.0
60 65 70 75 80 85 90 95 00 05
(log) real exchange rate
0.6
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60 65 70 75 80 85 90 95 00 05
(log) GDP per capita
-8
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0
4
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12
60 65 70 75 80 85 90 95 00 05
rate of growth GDP
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0
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current Account (% GDP)
-.6
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cumulative current account (% GDP)
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0
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60 65 70 75 80 85 90 95 00 05
real interest rate differential
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It is not our goal to describe in detail the reasons responsible for the Mexican collapsesbut rather to find the reasons for the appreciation of the Mexican peso, in the understand-ing that this issue influences the economy. Thus, we propose, firstly, that the appreciationis, to a big extend, result of the higher productivity growth in Mexico compared to itsmain economic partner, United States. Second, not only the BS effect is important toexplain the misalignments of the exchange rate, but also the evolution of other economicfundamentals, especially those related to capital flows, and the sustainability of the ex-ternal position of the economy are important.
Indeed, external shocks to the asset markets in the form of capital flow shifts or interestrate changes play key roles. In particular, the typical boom and bust cycle in Mexico overthis period began with an external shock: a fall in world interest rates or a liberalizationof trade or capital flows. This shock was normally followed by large capital inflows,increased fiscal expenditures (typically deficit financed), an expansion of the domesticmoney supply, higher inflation and an appreciation of the real exchange rate.
3 Modelling real exchange rates in Mexico
With the purpose of analyzing the evolution and the main determinants of the real ex-change rate in Mexico from 1960 to 2005, we first examine the empirical evidence for thepurchasing power parity hypothesis. Second, we propose an underlying relationship be-tween the real exchange rate, the relative labor productivity (i.e. the Balassa-Samuelsoneffect), the capital flows (proxied by the Capital Account) and the relative interest rate.These fundamentals were determined by three considerations; theory, availability of dataand whether the variable fits well in the model in statistical terms.
3.1 Data sources and construction of the variables
For the analysis we employed annual data for the period 1960-2005, collected from differentsources. We used the average nominal exchange rate, S (expressed as domestic currencyper US dollar) provided by the Banco de Mexico (Banxico) and the IMF InternationalFinancial Statistics (IFS). Both the Mexican and the U.S. GDP deflators (P and P*respectively, 2000=100) were also provided by the IFS. The real exchange rate series wasthen built on the former data, and it was defined as the ratio between the U.S to theMexican price index, expressed in Mexican pesos, i.e. RER = S(P ∗/P ). We worked withits logarithm and name this variable as q10.
To proxy the sectoral productivity differential (the BS effect) we constructed a seriesfor the logarithm of the real GDP per capita differential between Mexico and the U.S.(labelled as gdppc) using the index of the GDP’s volume (base year 2000) and the annualpopulation available at IFS.
For the interest rate in Mexico, we averaged the monthly time deposit rate until1978 and the 3-month CETES (Certificate of deposit) from that year on, both providedby Banxico. For the United States, we used the 10 years government bond yield. Weadjusted for inflation in each case by the consumer price index (CPI). The real interestrate differential (RIR) was obtained as the difference between the Mexican and the U.Sreal interest rate.
10Under this definition, an increase (decrease) implies a depreciation (appreciation).
8
Finally, to give account of the net foreign asset position we used the accumulatedcurrent account position as a percentatge of GDP, with the accumulation starting from1950. This measurement of the stock of foreign assets is similar in definition and closelyfollows the trajectory of the CUMCA variable used by Lane and Milessi-Ferreti (1999).However, our definition ignores the initial value as well as the effects of debt reduction.Yet, since we have a sufficiently long period of accumulation for the current account,cumulative flows provide a reasonable estimate of the underlying net foreign asset positionproviding the best measure available for the longer term horizon analyzed in this paper.
3.2 Empirical Analysis
To study the purchasing power parity we limited ourselves to test the non-stationarity ofthe real exchange rate11. Also, given that the PPP entail that in the long-run the realexchange rate converges to a constant mean, we propose that a simple test for structuralchange in the real exchange rate sets up an indirect way to examine for the PPP theory.
At this respect, it is worth mentioning that most of the empirical studies have focusedon examining the presence or absence of PPP, so the null hypothesis has been eitherthe stationarity or not-stationarity of the series. Nonetheless, these kinds of approaches,which reflect only one possibility, ignore valuable information, a fact that underminestheir own outcomes.
Therefore, with the purpose to evaluate the presence (or absence) of PPP as a long-runequilibrium value, we have used two different kinds of tests based on the residuals. Thefirst one, which includes the standard Dickey-Fuller (DF and ADF) and Phillips-Perron(PP) tests, have as the null hypothesis the non-stationarity of the RER. The second, onthe contrary, proposed by Kwiatkowski, Phillips, Schmidt, and Shin (1992), the KPSStest, uses as the null hypothesis the stationarity of the series.
[INSERT table 1]
11Surveys of the most important tests can be found in Froot and Rogoff (1995) and in Sarno and Taylor(2002).
9
Table 1: Unit root test in q and ∆q
Test Constant Constant & Trendq ∆q q ∆q
DF 2.13 5.48 2.67 5.42DFA 1.73 6.37 2.34 6.31PP 2.18 5.38 2.77 5.30KPSS 0.59** 0.04 0.18** 0.03
Note: (1) q: (log) real exchange rate; ∆q: first difference of q; (2) *,**,*** indicates the rejection of thenull hypothesis at the 1%,5% and 10% significance level, respectively.
10
Table 1 present the results of the unit root tests in the logarithm of the RER (q) andits first difference (∆q). It is easy to verify that there is no evidence to reject the nullhypothesis of one unit root in the real exchange rate (or reject the null hypothesis ofstationarity in the KPSS test) both including a constant and a constant and a time trend.
In addition, given that under PPP the rate of currency depreciation is nearly equalto the difference between the domestic and foreign inflation rates, a fact that is reflectedin the long-run in a stable real exchange rate, the simple presence of structural breaks inthe RER could be taken as evidence against the PPP. In other words, we propose thattesting for structural breaks in the real exchange rate sets up an indirect way to test forthe purchasing power parity hypothesis.
At this respect, a quick inspection of the evolution of the RER (see figure 1) revealsabrupt changes, at least in the mean, of the series. However, to confirm that effect, weperformed the test suggested by Bai and Perron (1998) to detect breaks. Briefly, thisapproach consists on detecting multiple structural changes in a linear regression modelestimated by minimizing the sum of squares residuals. The tests allows the time series tohave different numbers of breaks located at different dates. Given a maximum number ofunknown break points (mmax), it consists in estimating their position for each m≤m
max,testing for the significance of the breaks.
Once the dates for all possible m≤mmax are estimated, the point is to select the
suitable number of structural breaks, if any. Bai and Perron (1998) suggest, among otherprocedures, to use the modified Schwarz Information Criteria (LWZ) and the BayesianInformation Criteria (BIC) to select the final number of breaks.
Following this approach, we applied the procedure with a constant and a time trendand account for potential serial correlation via non-parametric adjustment12. By allowingup to 5 breaks and using a trimming of 0.15, both the LWZ and the BIC select three breaksin the real exchange rate13. The dates of the breaks are 1981, 1987 and 1994. Notice thatthe years coincide or precede the major economic crisis of the Mexican economy.
Therefore, the fact that the real exchange rate is not an immutable number has, at leasttwo important implications. First, the PPP cannot be considered as an anchor to decideover or under valuations. Second, the real exchange rate is influenced by macroeconomicfundamental variables that determine its evolution in the long-run.
Thus, we identified three fundamentals for the evolution of the RER: the sectoralproductivity differential (proxied by the relative GDP per capita), the movements of theinternational financial flows (proxied by the accumulated capital account) and the relativeinterest rate. The previous statement can be expressed as follows:
qt = β0 + β1gdppct + β2RIR + β3CCAt + εt (1)
Where εt is an i.i.d process, qt is the logarithm of the real exchange rate, gdppct is thelogarithm of the ratio of the Mexican to U.S real GDP per capita, RIRt is the real interestrate differential and CCAt is the ratio of the accumulated current account to GDP.
The standard approach would be to test if there exists a cointegration relationshipbetween the real exchange rate and the economic fundamentals. Nonetheless, the variablesshow different types of nonstationary behavior, not necessary corresponding to the unitroot hypothesis. Indeed, the results of the ADF, PP and KPSS tests show that while the
12The heteroscedasticity and autocorrelation consistent covariance matrix is constructed following An-drews (1991) using a quadratic kernel with automatic bandwidth selection based on an AR(1) approxi-mation.
13The trimming suggests the minimum distance between breaks
11
real exchange rate, the GDP differential and the capital account are I(1) variables, thereal interest rate is stationary14. In this case, the classical methods, such as the Johansencointegration procedure, would yield misleading conclusions15.
Thus, since an alternative cointegration testing approach is needed, we employed theautoregressive distributed (ARDL) bounds test as proposed by Pesaran, Smith, and Shin(2001). The choice of this test (PSS from now on) is based on the following considerations.Firstly, unlike most of the conventional multivariate cointegration procedures, which arevalid for large sample size, the bound test is suitable for a small sample size study.Secondly, the bound test does not impose restrictive assumptions that all the variablesunder study must be integrated of the same order. Its asymptotic distribution for the F -statistic is non-standard under the null hypothesis of no cointegration relationship betweenthe examined variables, irrespective whether the explanatory variables are purely I(0) orI(1), or mutually cointegrated. As such, the order of integration is no more a sensitiveissue and thus one could bypass the unit root test.
One interesting feature of the ARDL model is that it takes into account the errorcorrection term in its lagged period. The analysis of error corrections and autoregressivelags fully covers both the long-run and short-run relationships of the variables tested.As the error correction term in the ARDL does not have restricted error corrections, theARDL is an Unrestricted Error Correction Model.
The bound tests of proposed by PSS applies the fundamental principles of Johansen’sfive error correction multi-variance VAR models. Considering the presence of constant,time trend, and restricted condition, PSS distinguish five cases of interest delineatedaccording to how the deterministic components are specified: case I implies no interceptsand no trend; case II restricts intercepts but allows no trends; case III allows unrestrictedconstant and no trends; case IV considers unrestricted intercepts and restricted trendsand finally, case V involves unrestricted intercepts and trends.
For our particular purpose, the conditional equilibrium correction model (ECM) canbe written:
∆qt = co + c1t+ πqqqt−1 + πqxxxt−1 +
p−1∑i=1
Ψ′
i∆zt−i + δ′∆xt + υt (2)
Where z = (qt, gdppct, RIRt, CCAt)′ = (qt, x
′t). We ”bounds tested” for the presence
of a long-run relationship between the real exchange rate and the GDP differential, thereal interest rate and the capital account balance, using two separate statistics. The firstinvolves and F-test on the joint null hypothesis that the coefficients on the level variablesare jointly equal to zero. The second is a t-test on the lagged level dependent variable.
It is important to notice that instead of the conventional critical values, this testinvolves two asymptotic critical value bounds, depending on the dimension and cointe-gration rank, k and r, of the forcing variables xt as well as on whether restrictions areplaced upon the intercept and trend in (2). In particular, they show that the criticalvalues take on lower and upper bounds when r = k and r = 0 respectively. These twosets of critical values thus provide critical value bounds covering all possible classifications
14To save space, we do not report the results of these tests, but they are available upon request to theauthors.
15A series of studies by Pesaran and Shin (1995b), Pesaran and Shin (1995a), Pesaran, Smith, andShin (1996) and Pesaran, Smith, and Shin (2001) argued that as long as both I(0) and I(1) series existin a system, conventional cointegration tests, i.e., Johansen’s maximum likelihood approximation mightbias the results of the long-run equilibrium interactions among variables.
12
of into I(0), I(1) and mutually cointegrated processes. The PSS test is then formulatedas follows:
H0 : πqq = 0 and H0 : πqxx = 0
against
H0 : πqq 6= 0 and H0 : πqxx 6= 0
If the computed statistic exceeds their respective upper critical values, then there isevidence of a long-run relationship regardless of the order of integration of the variables.If, on the contrary, it is below, it is not possible to reject the null hypothesis of nocointegration and if it lies between the bounds, any inference is inconclusive. If thetest statistic exceeds its upper bound, then we reject the null of no cointegration. Theprocedure then amounts to test the assumption of no relationship (in levels) between thedependent variable q and the independent variables xt−1 in the regression.
Some important issues in the specification are whether to include a deterministic trendin the ECM, and the number of lags, p, to include in the regression. Since the test isbased on the assumption that the disturbances are serially uncorrelated, this is not atrivial issue. Thus, as noted by Pesaran, Smith, and Shin (2001), for the bound test tobe valid, it is especially important to ensure that there is no serial correlation.
It is clear from figure 1 that only the real exchange rate shows a declining trend.This suggests, at least initially, that a restricted linear trend should be included in theequation. To determine the appropriate lag length, we estimated the conditional model (2)by LS, with and without a linear time trend and a constant. Allowing for a maximum laglength of two, we selected the ARDL model based on the Schwartz’s Bayesian InformationCriteria (SBC) and Lagrange Multiplies (LM) statistics for testing the hypothesis of noserial correlation against orders 1 and 2.
Given that neither the constant nor the trend (unrestricted or restricted to the real ex-change rate) were significant, our relevant model is case I in PSS. However, we also presentthe results from the ARDL model when a constant and the restricted trend are included(case IV). Based on the different criteria, the final model selected is an ARDL(0,0,2,1)and an ARDL(1,0,1,0) for case I and case IV, respectively. Although the noticeably in-consistent results when mixing I(0) and I(1) series, we also used Johansen’s methodologyto test for cointegration among the variables. We present the λ (test of the maximumeigenvalue) and the trace statistic of the cointegration test among the variables. Table 2summarizes the results.
[INSERT table 2]
13
Table 2: Bounds cointegration and Johansen cointegration tests between the(log) real exchange rate and fundamentals
Bounds cointegration tests FI tI χ2BG(2)
Case I: no constant or trend 4.122** 3.491** 0.244(0.784)
Case IV: constant & restricted trend 4.475** 1.581(0.220)
Johansen cointegration tests Trace λr=0 57.100* 36.805*r≤1 20.294 12.488r≤2 7.806 6.613r≤3 1.192 3.841
Note: (1) FI and FIV are the F -statistic for testing H0 : πqq = 0 and H0 : πqxx = 0 in eq. (2) when nolinear trend and constant and restricted trend, respectively, are included in the equation; (2) tI is thet-ratios for testing H0 : πqq = 0 in eq. (2) without a linear trend; (3) ** indicates that the statistic isabove the 5% upper bound; (4) Critical values from Pesaran, Smith, and Shin (2001); (6) χ2
BG(2) is theBreusch and Godfrey statistics for serial correlation at order 2 and its p-values is in parenthesis; (7) InJohansen test, H0 = rango(Σ) = r; (8) λ: test of the maximum eigenvalue; (9) * denotes rejection of thehypothesis at the 0.05 level.
14
As it can be seen, the results from the PSS test indicate the presence of a valid long-runrelationship between the real exchange rate and the explanatory variables, as the F -teststatistics, exceed the respective upper critical values both, when no trend or constantare included and when the trend is restricted. The result from the application of thebounds t-test to the real exchange rate equation is also clear, since the value of the teststatistic lies above the 5% critical values. Hence, based on both, the F -test and the t-test,we can reject the null hypothesis of no cointegration, regardless of whether the variablesare I(0), I(1) or a mix of both. Care should be, however, be taken with respect to theinterpretation of the output obtained with these, the Johansen tests confirm the presenceof the long-run relationship.
In the previous specifications, it is important that the coefficients of lagged changesremain unrestricted, otherwise these tests could be subject to a pre-testing problem.Nonetheless, following PSS, for the subsequent estimation of level effects and short-rundynamics of the real exchange rate, we use of a more parsimonious specification. Theestimated error correction model is presented in table (3)16.
[INSERT table 3]
16We introduced a dummy variable for the years 1986 and 1987 (d8687) to account for the effects ofsome economic events that took place in those years. In particular, at the end of 1986 there was animportant reduction in the oil international prices and, therefore in the value of the Mexican exports.Second, both, interest rates and the inflation increased considerably. As a result, the economic activitywas reduced about 3% in 1987.
15
Table 3: Equilibrium Correction Model for the (log) real exchange rate
Dependent variable: Coeficient t-value∆(q)
Long-run terms:Equilibrium error -0.397 -3.106Constant 0.716 2.506gdppct−1 -1.171 -4.756CCAt−1 -1.307 -2.123RIRt−1 -0.016 -4.074
Dynamic terms:∆gdppct 0.699 0.227∆CCAt -1.350 -5.197∆RIRt -0.002 -2.111∆RIRt−1 0.001 1.793d8687 0.2420 3.627
R2: 0.767χ2
BG(2): 1.123(0.337)Note: (1) q is the (log) real exchange rate, gdppc is the (log) constant GDP per capita differential, CCA
is the cumulative current account (as % of GDP), RIR is the real interest rate differential and d8687 is adummy variable that takes value 1 over the years 1986 and 1987, 0 elsewhere; (2)∆ is the first differenceoperator; (3) χ2
BG(2) is the Breusch and Godfrey statistics for serial correlation at order 2 and its p-valueis in parenthesis.
The short and long-run dynamics of the real exchange rate are then fully capture by thespecification presented in table 3. Several aspects are important about this model. As itcan be seen, all level estimates are significant and have the expected signs, indicating first,that in the long-run a rise in the relative GDP per capita (or productivity) leads to a realexchange rate appreciation, as suggested by the Balassa-Samuelson hypothesis. Second,an improve of the net foreign asset position (i.e. lower indebtedness) is also associatedwith a real appreciation in the long-run. Third, a higher interest rate in relation to theworld interest rate generates an excess demand for foreign currency that will turn into aweaker domestic currency.
In addition to the long-run effects, temporary changes in the fundamentals also haveshort-run effects. This becomes evident by the negative effect that both, the contempo-raneous stock of foreign assets and the real interest rate, have on the real exchange rate.Indeed, capital inflows are important in the immediate short-run via the influence of theshort-run flows, which lead to a real appreciation. Surprises, however, the positive signof the lagged change in the interest rate. Yet, the associated t-statistic fails to meet thefive-percent criterion, preventing any meaningful conclusion. On the contrary, while thelevel effect of productivity differential is important, the short-run effect of this variable isnot significant.
Finally, a key parameter in the previous estimation is the associated with the equi-librium correction term, since it measures the degree of adjustment of the actual realexchange rate with its equilibrium level. We found that the speed of adjustment is signif-icant, indicating that about 40% of the adjustment takes place within a year17.
17Notice, however, that in a specification as the one presented in table (3) there might be simultaneousfeed-back effects from ∆(lgdpt), ∆(KABt) and (RIRt) so that the OLS estimates might suffer fromsimultaneity bias. To overcome this, we tried to estimate the equation with instrumental variables, butwe failed to obtain reliable results from this methodology.
16
3.3 Impulse response function
We presented evidence earlier that the real exchange rate is cointegrated with the economicfundamentals and that, as a results of the variability in these factors, the exchange rate issubject to permanent changes. Yet, a sensible way to gain a full insight into the relativeimportance and persistence that shocks in the shocks in the productivity, the interestrate and the current account have in the real exchange rate is through impulse responsefunctions.
The idea of impulse response functions is to examine the effects of one standard de-viation shock on the contemporaneous and future values of the endogenous variables ina model. For construction, the results of the impulse response function are subject tothe ”orthogonality” assumption and might differ markedly depending on the ordering ofthe variables in the VAR. Yet, a simple way to overcome this is to employ the general-ized impulse response function (GI), suggested by Koop, Pesaran, and Potter (1996) andPesaran and Shin (1998).
The GI does not require the orthogonalization of the innovations and does not dependof the ordering of the variables in the model. Briefly, the idea is to obtain a media of thefuture shocks in a way that the response is an average of what could happened given thepresent and the past. Given an actual arbitrary shock, δk, in the k variable, the GI isdefined as:
GI[n, δk,Ωt−1] = E[yt+n | εkt,Ωt−1]− E[yt+n | Ωt−1] (3)
Where n is the number of periods ahead, δk = (σkk)1/2 denotes one standard error
shock, Ωt−1 is all the information available in the moment of the shock (i.e. the knownhistory of the economy up to the moment t − 1), E[·|·] is the conditional mathematicalexpectation taken with respect to the VAR model and εkt are the original innovations inthe VAR. In opposition to the standard impulse response function, in the GI all contem-poraneous and future shocks are integrated out. Thus, the generalized impulse responsefunction for the y vector n periods ahead is the difference between the expected value ofyt+n when the δk shock is taken into account and the expected value without the shock.Assuming Gaussian errors, Koop, Pesaran, and Potter (1996) show that the conditionalexpectation of the shock is equal to:
E[εt|εkt = δk] = (σ1k, σ2k, ..., σmk)′ − σ−1
kk δk = Σejσjj−1δj (4)
where ek is the selected vector with the k-th element equal to one and all other elementsequal to zero and Σ = E(εtε
′t). Then, the GI for a one standard deviation shock, δk = 1,
to the k variable is:
γk(n) = ψnΣekσ−1kk (5)
Thus, given the historic distribution in the residuals, it is important to notice that aone shock in the k-th equation implies shocks in the other equations as well. In this way,the generalized impulse response does not pretend to answer what would happened if thereis one shock with ”all other thing remaining equal”. It is rather the historical distributionof residuals (as expressed in the variance and covariance matrix) which determines theeffects of the impact of other variables.
Figure 2 displays the results of the generalized impulse response function for tendifferent forecasting horizon obtained from a VAR that includes the (log) real exchange
17
rate, the (log) GDP per capita differential, the accumulated capital account (as %of GDP)and the real interest rate differential18. In all specifications, the VAR includes one lagand a constant as the only exogenous variable.
[INSERT figure 2]
18Because we are focussing on the fluctuations in the real exchange rate, we only report the results forthe real exchange rate and analyze the relative importance of the different factors in the model.
18
Figure 2: Generalized impulse response function of the (log) real exchange rate to an inno-vation in the (log) real GDP per capita differential, cumulative current account (%GDP)and real interest rate differential
-.15
-.10
-.05
.00
.05
.10
.15
1 2 3 4 5 6 7 8 9 10
Response of q to q
-.15
-.10
-.05
.00
.05
.10
.15
1 2 3 4 5 6 7 8 9 10
Response of q to CCA
-.15
-.10
-.05
.00
.05
.10
.15
1 2 3 4 5 6 7 8 9 10
Response of q to RIR
-.15
-.10
-.05
.00
.05
.10
.15
1 2 3 4 5 6 7 8 9 10
Response of q to gdppc
Response to Generalized One S.D. Innovations ± 2 S.E.
Notes: (1) q is the (log) real exchange rate, gdppc is the (log) constant GDP per capitadifferential, CCA is the cumulative current account (as % of GDP) and RIR is thereal interest rate differential; (2) VAR includes constant and one lag.; (3) the doted lineindicates one standard deviation ± 2 standard errors
19
As it can be seen, a one standard deviation impulse in the GDP per capita differentialhas a negative effect on the real exchange rate. That is, one shock in the productivityinduces a real appreciation that tends to diminish gradually. Also, an increase in thestock of net foreign assets has a lasting negative effect on the real exchange rate. Finally,a one shock in the real interest rate has a minor effect on the real exchange rate.
20
4 Concluding remarks
Conventional models assume the real exchange rate is determined by a certain form ofthe purchasing power parity condition. According to PPP, a country has an overvaluatedcurrency when its domestic inflation exceeds that of its trade partners. It is preciselythis what produces a lost in price competitiveness and, as a result, a trade deficit in thebalance of payments. Therefore, to correct this deficit, the nominal exchange rate mustadjust.
Therefore, under the PPP doctrine, and given the mean reversion mechanism, realand nominal exchange rates cannot be misaligned for long periods of time. However, theempirical evidence, not only in Mexico, but in most of the countries, shows that this isnot the case. The challenge in this case would be to explain the long periods of currencyappreciation or depreciation as well as the long-lasting misalignments of the real exchangerates.
According to this, we analyzed the short and long-run determinants of the real ex-change rate in Mexico between 1960 and 2005, finding, first, that the purchasing powerparity cannot be taken as a long-run equilibrium relationship. In addition, we found thatthe real exchange rate, far from converging to a constant mean overtime, was subject toseveral structural breaks which correspond to the main economic crisis in Mexico.
The fact the exchange rate does not adjust to achieve and maintain competitivenesshas to be explained within a broader context. Thus, based on equilibrium exchange rateparadigms, we found out that the real exchange rate in Mexico is connected to macroeco-nomic variables such as the relative productivity, the real interest rate and the stock oddebt of a country. We provided an analysis of the long and short-run co-movements be-tween the real exchange rate and these set of economic fundamentals finding a reasonableexplanation for the real exchange rate appreciation.
So, as revealed by the VAR approximation and the estimation of impulse-responsefunction, productivity differentials are important. Indeed, the differences in the economicgrowth between Mexico and United States resulted in an appreciation of the currency ofthe faster-growing country, Mexico.
However, at least two things are clear. First, the higher evolution of the productivityin Mexico vis-a-vis USA in some years contributed to the appreciation of the Mexicancurrency. However, it is likely that such an effect had a stronger influence between 1960and late 1970’s, when the income gap between both countries shrank. This catching-upended with the 1982 economic crisis, from whence the BS impact might had declined.
Nowadays, more crucial for the exchange rates movements in Mexico and in otherdeveloping economies are the effects of the interest rates and the size of the net foreignassets, especially in a period driven by the twin forces of globalization and liberalizationof markets and trade. First, in recent years, many emerging economies have graduallyrelaxed or removed capital controls. Second, many of these economies have accumulatednet foreign liabilities. In general, in these countries, upward pressure on the exchangerate has stemmed largely from the increased in capital movements19.
Indeed, we found evidence first, that a higher interest rate generates an inflow ofcapitals which, in turns, appreciates the real exchange rate. Second, the size of netforeign assets is associated with a more appreciated exchange rate. That is, reaching ahigher level of net foreign assets can afford to finance a worse current account balance
19The vulnerability of the small open economies to capital flows reversal is highlighted by, for example,the Mexican peso crisis of 1994-95.
21
and therefore can sustain a loss in competitiveness associated with a more appreciatedreal exchange rate.
In addition, the link between exchange rates and foreign sector imbalances and interestrates is also important in the short-run and when one considers the expectations of theexchange-rate market participants. Indeed, changes in the expectations, usually caused bycurrent account imbalances (triggered either by trade flows or domestic saving-investmentdisequilibrium) can bring sudden and frequent adjustments in portfolios, which lead toexchange rate movements. For instance, when a country runs an unsustainable currentaccount deficit (surplus) it loses (accumulates) foreign bonds and reduces its internationalreserves. In this case, agents anticipate a currency depreciation that will, eventually, takeplace if doubt amounts to a relevant level20.
The fact that the real exchange rate will change in response to a set of economicfundamentals have several policy implications. For example, given the link between theexchange rate and the capital flows, managing of the capital transactions will have perma-nent effects on the real exchange rate. Since there is much room for policy intervention,attention must be given to productivity, interest rates and capital movements, when con-sidering exchange rate objectives. Our analysis suggests that, whatever exchange rateregime a country follows, long-term success depends on a commitment to sound economicfundamentals. This is not only the case for Mexico but also for other developing countries.
Finally, we want to address that failure to reject the unit root hypothesis by a linearautoregressive process for the real exchange rate does not necessarily invalidate the pur-chasing power parity hypothesis. Indeed, a necessary condition for the weak form of PPPto hold in the long-run is that the real exchange rate, without any parameter restriction,is stationary. However, failure to reject the unit root hypothesis might imply that thetrue process for the exchange rate is given by a nonlinear model. This might open a veryinteresting field for future research.
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